\[ \begin{aligned} \frac{\partial}{\partial x} \left[ - (x - 3y)^2 \right] &= -2(x - 3y) \frac{\partial}{\partial x}(x - 3y) \\ &= -2(x - 3y) \left[ \frac{\partial}{\partial x}(x) - 3\frac{\partial}{\partial x}(y) \right] \\ &= -2(x - 3y)[1 - 3(0)] \\ &= -2(x - 3y) \end{aligned} \]
\[ \begin{aligned} \frac{\partial}{\partial y} \left[ - (x - 3y)^2 \right] &= -2(x - 3y) \frac{\partial}{\partial y}(x - 3y) \\ &= -2(x - 3y) \left[ \frac{\partial}{\partial y}(x) - 3\frac{\partial}{\partial y}(y) \right] \\ &= -2(x - 3y)[0 - 3(1)] \\ &= 6(x - 3y) \end{aligned} \]